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GCSE Maths / Edexcel

Angle facts

Use angles on a straight line, around a point, vertically opposite angles, and triangle angle sums to find missing angles.

Geometry and MeasuresFoundation and HigherGrades 2 to 5Focused skill

Curriculum path: GCSE Maths > Edexcel > Geometry and Measures > Angle facts

Pearson Edexcel GCSE Maths geometry G3 and G4: use angle facts, properties of lines, triangles and quadrilaterals.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Angle fact questions are usually about choosing the right fact before doing the arithmetic.

Angles on a straight line add to 180 degrees. This is often used when two angles sit next to each other on one line.

Angles around a point add to 360 degrees. If several angles meet at one point, add the known angles and subtract from 360.

Vertically opposite angles are equal. They are the angles opposite each other when two straight lines cross.

Angles inside a triangle add to 180 degrees. For Foundation students, this is one of the most important geometry facts to remember.

For Edexcel marks, write the angle fact in words or show it clearly in the calculation.

Key ruleStraight line = 180 degrees, around a point = 360 degrees, triangle = 180 degrees.

Diagram guide

65°115°straight line65° + 115° = 180°
Angles on a straight lineThe two adjacent angles sit on one straight line, so they must add to 180 degrees.
90°125°xAll angles around one point add to 360°known angles + x = 360°
Angles around a pointAll the angles meeting at one point make a full turn, so they add to 360 degrees.
54°76°x54° + 76° + x = 180°
Angles in a triangleThe three interior angles in every triangle add to 180 degrees.
72°xOpposite angles made by crossing lines are equal.
Vertically opposite anglesWhen two straight lines cross, opposite angles are equal.

Worked examples

Straight line

Two angles on a straight line are 68 degrees and x. Find x.

65°115°straight line65° + 115° = 180°
Example: straight lineThe two adjacent angles lie on a straight line, so their total is 180 degrees.
  1. Angles on a straight line add to 180 degrees.
  2. x = 180 - 68.
  3. x = 112 degrees.

Answer: 112 degrees

Around a point

Angles around a point are 90 degrees, 125 degrees and x. Find x.

90°125°xAll angles around one point add to 360°known angles + x = 360°
Example: around a pointAll angles around the centre point add to 360 degrees.
  1. Angles around a point add to 360 degrees.
  2. 90 + 125 = 215.
  3. x = 360 - 215.

Answer: 145 degrees

Triangle

A triangle has angles 54 degrees, 76 degrees and x. Find x.

54°76°x54° + 76° + x = 180°
Example: triangle angle sumThe three angles inside the triangle add to 180 degrees.
  1. Angles in a triangle add to 180 degrees.
  2. 54 + 76 = 130.
  3. x = 180 - 130.

Answer: 50 degrees

Common mistakes

  • Using 360 degrees for a straight line instead of 180 degrees.
  • Forgetting that vertically opposite angles are equal.
  • Adding the known angles but not subtracting from the total.
  • Giving an answer without explaining which angle fact was used.

Quick exercise

Try these before moving to the exam-style questions.

  1. Angles on a straight line are 47 degrees and x. Find x.
    65°115°straight line65° + 115° = 180°
    Quick check: straight lineSubtract the known angle from 180 degrees.
  2. Angles around a point are 80 degrees, 110 degrees and x. Find x.
    90°125°xAll angles around one point add to 360°known angles + x = 360°
    Quick check: around a pointKnown angles plus the missing angle must total 360 degrees.
  3. A triangle has angles 35 degrees and 65 degrees. Find the third angle.
    54°76°x54° + 76° + x = 180°
    Quick check: triangleThe three interior angles must total 180 degrees.
  4. Two vertically opposite angles are labelled 72 degrees and x. Find x.
    72°xOpposite angles made by crossing lines are equal.
    Quick check: vertically oppositeOpposite angles made by crossing straight lines are equal.
  5. A quadrilateral has angles 90 degrees, 100 degrees, 85 degrees and x. Find x.
    90°100°85°xAll four interior angles add to 360°
    Quick check: quadrilateralThe four interior angles in a quadrilateral add to 360 degrees.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Two angles on a straight line are 63 degrees and x. Work out x.

65°115°straight line65° + 115° = 180°
Question diagram: straight lineThe two angles sit on one straight line, so use 180 degrees.
angle factsstraight linefoundation geometry
Standard exam styleFoundation and HigherNon-calculator3 marks

Three angles around a point are 94 degrees, 121 degrees and x. Work out x.

90°125°xAll angles around one point add to 360°known angles + x = 360°
Question diagram: around a pointAll the angles around the centre point add to 360 degrees.
angles around a pointmissing anglemethod marks
ChallengeFoundation and HigherEither4 marks

A triangle has one angle of 48 degrees. The other two angles are equal. Work out the size of each equal angle.

54°76°x54° + 76° + x = 180°
Question diagram: equal triangle anglesSubtract the known angle from 180 degrees, then share the remaining angle equally.
triangle anglesisosceles trianglemulti-step angle